Kitaev Toric Code — Topological Error Correction

The toric code is a topological quantum error-correcting code on a 2D lattice where qubits live on edges. Vertex operators A_v = ∏ σˣ and plaquette operators B_p = ∏ σᶻ detect errors without revealing the encoded logical qubits. Anyonic excitations (e and m particles) created by errors must be paired and annihilated to correct them.

e-anyon (vertex violation)
m-anyon (plaquette violation)
flipped qubit (error)
p = 0.030
7 × 7